Question

You are considering making a one-time deposit of $2,197 today, in a bank that offers an interest rate of 9% APR. If you leave your money invested for 5 years, how much money will you have at the end of this period? Consider monthly compounding. Enter your answer in terms of dollars and cents, rounded to 2 decimals, and without the dollar sign. That means, for example, that if your answer is $127.5678, you must enter 127.57

Answer 1

After depositing $2,197 in a bank account with a 9% annual interest rate compounded monthly for 5 years, the future value of the investment will be $3,439.35.

Step-by-step explanation:

To calculate the future value of a one-time deposit using compound interest with monthly compounding, we use the formula Future Value = Principal × (1 + (Interest Rate / Number of Compounding Periods))^(Number of Compounding Periods × Time in Years). Given a principal of $2,197, an annual interest rate (APR) of 9%, and monthly compounding, the formula will look like this:

Future Value = 2,197 × (1 + (0.09 / 12))^(12 × 5)

Calculating the above expression, we find:

Future Value = 2,197 × (1 + 0.0075)^(60)

Future Value = 2,197 × (1.0075)^(60)

Future Value = 2,197 × 1.565678

Future Value = $3,439.35

Thus, after 5 years with monthly compounding at a 9% annual interest rate, you will have $3,439.35.